A vacuum pump has a cylinder of volume upsilon and is connected to a vessel of volume `V` to pump out air from the vessel The initial pressure of gas in vessel is `P` Show that after n strockes the pressure in vessel is reduced to
`P_(n) = P[(V)/(V+v)]^(n)` .

Explanation

Let pressure of gas left in vessle after I operation be `p_(1)` Let `n_(1)` moles are removed from vessel after I operation Let n mole were present initially Thus initial state `PV =nRT`
`:. P_(1)V =(n-n_(1))RT`
`P_(1)V =nRT -n_(1)RT`
`P_(1) V =PV -n_(1)RT`
The `n_(1)` mole taken out has volume v at pressure `P_(10` Thus
By eps (3) and (4) `P_(1) V =PV-P_(1)upsilon`
or `P_(1) = P[(V)/(V +upsilon)]..(5)`
Similarly for II operation
`P_(2) =P_(1) [(V)/(V +upsilon)]=P[(V)/(V+upsilon)]^(2)`
Thus for n operation
`P_(n) =PP_(2) =P_(1) [(V)/(V +upsilon)]^(n)` .